The following question from NJCTL was assigned for me as homework. It is not a heavy computational problem, but rather, a conceptual one. I reviewed the meta guide regarding these types of questions and so I hope this is appropriate.
An object starts at rest and accelerates at a constant rate in a circular path. After a certain time $t$, the object reaches the angular velocity $\omega$. How many revolutions did it make over time $t$?
The supplied answer, in general terms of course, is $\omega t/4\pi$. I do not understand this type of problem conceptually and an internet search for this type of problem did no avail.
What made sense to me was to pick an arbitrary angular acceleration $\alpha$ and make a list of angular velocities.
My attempt with some casework:
Letting $\alpha=3$ revolutions$/s^2$ we have the following where $t$ is in seconds and $\omega$ is in revolutions per second.
Over this interval of $3$ seconds, we have an angular displacement of 18 revolutions.
My problem arises here. Angular displacement seems to be growing at a different rate than the solution gives. I am not sure how $\pi$ makes its way into the solution if I begin with revolutions rather than radians. I am looking to intuitively understand how this solution is formulated. I believe that I took the wrong approach, however, I cannot think of any other way to move forward with this.